We're dividing 677942 by 71 
Our goal is to divide 677942 by 71.

Going ahead to step 1:
The number 71 fits into 6 0 times, leaving a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Fetch the next digit (7) from the dividend, attach it to 6 and continue: 67 / 71

Going ahead to step 2:
71 goes into 67 0 times with a remainder of 67.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 67 leaves us with 67.
Bring next digit (7) of the dividend behind the 67 and repeat the process: 677 / 71

Advancing to step 3:
71 goes into 677 9 times with a remainder of 38.
The next digit of our result is 9. 
Result so far: 9.0
If we take 639 away from 677, we end up with 38.
Append the next digit (9) from the dividend to 38 and continue with: 389 / 71

Step 4:
71 can be fit into 389 5 times, resulting in a remainder of 34.
Put 5 as the next digit of the answer. 
Result so far: 95.0
Subtracting 355 from 389 leaves us with 34.
Append the next digit (4) from the dividend to 34 and continue with: 344 / 71

Step 5:
The number 71 fits into 344 4 times, leaving a remainder of 60.
The number 4 becomes the next digit in our result. 
Result so far: 954.0
If we take 284 away from 344, we end up with 60.
Take the next digit (2) from the dividend and append it to 60, then repeat: 602 / 71

Moving on to step 6:
The number 71 fits into 602 8 times, leaving a remainder of 34.
Record the quotient 8 as the next digit in the result. 
Result so far: 9548.0
Subtract 568 from 602 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 7:
71 goes into 340 4 times with a remainder of 56.
The number 4 becomes the next digit in our result. 
Result so far: 9548.4
The remainder is 56 after subtracting 284 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Step 8:
The number 71 fits into 560 7 times, leaving a remainder of 63.
The next digit of our result is 7. 
Result so far: 9548.47
If we subtract 497 from 560, we get 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Let's proceed to step 9:
71 can be fit into 630 8 times, resulting in a remainder of 62.
The number 8 becomes the next digit in our result. 
Result so far: 9548.478
If we subtract 568 from 630, we get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Let's proceed to step 10:
The number 71 fits into 620 8 times, leaving a remainder of 52.
The number 8 becomes the next digit in our result. 
Result so far: 9548.4788
Subtracting 568 from 620 leaves us with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

The final result is 9548.4788 with a remainder of 0.00052.